Nearly one in five adolescents currently live with a diagnosed mental or behavioral health condition, such as anxiety, depression, or conduct disorder, underscoring the urgency of developing accurate and interpretable diagnostic tools. Resting-state functional magnetic resonance imaging (rs-fMRI) provides a powerful lens into large-scale functional connectivity, where brain regions are modeled as nodes and inter-regional synchrony as edges, offering clinically relevant biomarkers for psychiatric disorders. While prior works use graph neural network (GNN) approaches for disorder prediction, they remain complex black-boxes, limiting their reliability and clinical translation. In this work, we propose CONCEPTNEURO, a concept-based diagnosis framework that leverages large language models (LLMs) and neurobiological domain knowledge to automatically generate, filter, and encode interpretable functional connectivity concepts. Each concept is represented as a structured subgraph linking specific brain regions, which are then passed through a concept classifier. Our design ensures predictions through clinically meaningful connectivity patterns, enabling both interpretability and strong predictive performance. Extensive experiments across multiple psychiatric disorder datasets demonstrate that CONCEPTNEURO-augmented GNNs consistently outperform their vanilla counterparts, improving accuracy while providing transparent, clinically aligned explanations. Furthermore, concept analyses highlight disorder-specific connectivity patterns that align with expert knowledge and suggest new hypotheses for future investigation, establishing CONCEPTNEURO as an interpretable, domain-informed framework for psychiatric disorder diagnosis.